Singular Laplacian Growth

Дата и время публикации : 1997-10-05T01:11:07Z

Авторы публикации и институты :
Mark A. Peterson (Mount Holyoke College)

Ссылка на журнал-издание: Ссылка на журнал-издание не найдена
Коментарии к cтатье: 8 pages, Latex, 4 figures, Submitted to Phys. Rev. E
Первичная категория: cond-mat.stat-mech

Все категории : cond-mat.stat-mech, cond-mat.dis-nn

Краткий обзор статьи: The general equations of motion for two dimensional Laplacian growth are derived using the conformal mapping method. In the singular case, all singularities of the conformal map are on the unit circle, and the map is a degenerate Schwarz-Christoffel map. The equations of motion describe the motions of these singularities. Despite the typical fractal-like outcomes of Laplacian growth processes, the equations of motion are shown to be not particularly sensitive to initial conditions. It is argued that the sensitivity of this system derives from a novel cause, the non-uniqueness of solutions to the differential system. By a mechanism of singularity creation, every solution can become more complex, even in the absence of noise, without violating the growth law. These processes are permitted, but are not required, meaning the equation of motion does not determine the motion, even in the small.

Category: Physics